Card Game: AP Stat Ideas

Below are 4 hands from the game "13" that my students now play all the time now that projects are getting finished and school is ending.  Apparently 2's are the best.  I don't know the rules, and I'm not certain they do either.  I believe you can play straights, multiple pairs of multiple numbers, I don't even know.  Do people besides students at my school play this game(i.e. do you know what a "cutup" is)?  An interesting way to analyze probability anyhow.  Here are 4 real hands dealt during a resource period.  Ideas...who will win?  who has the "best" hand

End of Year Project Topics

This is an incredibly interesting list of project ideas that my students have generated.  I thought I'd share what they're capable of when they have zero restrictions...

10-11 End of Year Project Ideas 

Some highlights if you don't feel like reading through the whole thing...

1. Mythbusters: Mac vs PC
2. Value of a Power Hitter or Contact Hitter in Fantasy Baseball
3. Developing software that is usable exclusively in an AP Stat class
4. Using a test vs. a qualitative measure to assess learning
5. Profiles of countries in a state of unrest to predict revolt (the wiki for this project)
6. Price differences between Ebay and craigslist
7. The chance of finding a 15 to 64 year old male in Luxembourg that is a noble compared to a similar-aged male in Denmark being a noble.  (easily the most unique project ever done)
8. Using Wikipedia, how long it takes for random words using the formula of always clicking the first blue, unbolded and unitalicized word, lead to the end word of Philosophy. On the theory that every word in Wikipedia will eventually lead to Philosphy. Words will be chosen via randomized dictionary words. (based on the fact that clicking the first blue, unbolded, unitalicized word of every page eventually leads to Philosophy)

With a little bit of freedom (okay, a lot of freedom) they come up with some awesome topics and they really enjoy their work in class during these couple of weeks.

How will I grade them?  By writing a list of what the student did well and what the student did not do well. 

A Farewell to Teaching

I'm writing this post to inform everyone that reads this (who knows how many) that at the end of this school year I will be making a career change.  I will be starting down the career path to becoming an actuary, which is a unique opportunity that I am extremely excited about.

I'd like to thank anyone that has taken the time to read this blog for allowing me to share some ideas about education that are unique.  I've continued to blog this year due to the amazing conversations that I've had with colleagues nation wide.  Most of you I've never met face to face, but I enjoyed having an audience to bounce some AP Stat and just general education reform ideas off of.  This is something I would not have done with anybody but my personal learning network on the internet.  Again, thank you.

Feel free to use any of my ideas in any capacity that you wish.  No need to be proprietary, as I'm all about moving education forward.  I encourage you to consult with and contribute to the class wiki that we've started this year, that will hopefully evolve into an online statistics resource for any and every statistics student that would be in need.

The Class Wiki: http://statknowledge.wikispaces.com

Will the blog continue?  Probably.  Just in a much different capacity and probably be more math nerd related than anything.  Again, to my PLN, thank you so much for contributing so much to my professional development. 

A Project per Unit: Understanding By Design in AP

Some project ideas for AP Statistics that are unit specific.  I'd begin each unit by asking these questions and having kids consider just what data they'll collect and how they'll answer these questions.  Then build all the statistics concepts around them as they come up, not as a series of "concepts".

Unit I: Displaying and Describing Data
1.  Market Research: design a product, determine the market for it, determine how much you should charge for it

• Create a coffee stand for your school building
• Pillow-pack: A backpack with a pillow built in to it

2.  Consumer Education: Choose a series of similar products and determine which one is the best for consumers

• I have a number of kids working on an end of the year project comparing all types of smartphones
• Mac vs PC?
• Tablet PC's

3.  What makes a song popular?

Unit II: Displaying and Describing Bivariate Data (probably my weakest ideas)
1.  Have them collect data that makes them think about what a correlation actually shows (not causation, only a relationship between two variables, etc)

• Caloric Intake vs Weight 
• Grams of Fat vs Grams of Protein consumed daily
• Income Level vs Achievement Level in Standardized tests (state tests, SAT's, AP, etc.)

Unit III: Collecting Data
1.  What's the best sample we can get to investigate one of these questions?  I want them to see just how poorly they collected data in Unit I and II

• What proportion of the school district has internet access?
• Revise their sampling methods from previous units

Unit IV: Probability
1.  Design a game of chance that is profitable (run them all together on a casino day complete with fake money to see how profitable it is in the short-run)

Unit V: Inference for Proportions
1.  Continue any of the data collections that were done in the beginning of the year, looking for significant differences (consumer education, market research) - introduces significance, might be boring.
2.  Is there equality that exists between schools/institutions?  What do "richer" schools have that "poorer" schools do not?  Why?
3.  Tell a joke and determine whether or not it is funny.  Possibly look at a comedian's standup routine to determine if they are funny
4.  Type I and Type II Error: Explore wrongful convictions.  Have them explore some court cases that are under contention (OJ Simpson, Mumia, etc) and some court cases that are open and shut (Bernie Madoff).

Unit VI: Inference for Means
1.  Is there an advantage to eating a raw vegan diet vs the traditional "Western" diet? Inspired by recent events as we have recently started a Raw Vegan diet (and have never felt better)
2.  Is there equality between schools/institutions?

Unit VII: Inference when Variables are Related (T-tests for Slope and Chi-Squared Tests)
1.  Should you choose one letter over another when taking a multiple choice test? (sorry for so many testing heavy examples)
2.  Do a t-test for slope on any of the bi-variate data collected in Unit II

Most of the inferential statistics can be applied to enhance the projects and work done in the beginning of the year.  See my post on Inferential Statistics Data Collection for others, and of course feel free to lend me your ideas.

Inferential Statistics: A Different Approach

For the longest time I've given thought to providing instruction on inferential statistics in a unique fashion.  If you're an AP Stat teacher, it means a departure from the One-Proportion Z-test, Two-Proportion Z-test, One Sample t-test, Two-Sample t-test, Matched Pair t-test, Chi-Squared Test(s), t-tests for slopes of regression lines.

So here's how I'd start...all data collection.  Spend a couple of days collecting data for each situation.  One of the essential questions I'd like my students to explore throughout the year is "Which model is the most appropriate for data you have collected?"  Here's where we go into depth about why certain models are more appropriate than others...

Data to Collect

1. Number of victories in 100(or so) games of Rock-Paper-Scissors
2. Toss a thumbtack and record proportion of "up" 
3. Drop a piece of buttered toast 50(or so) times and measure how many times it lands "buttered-side down"
4. Give a dummy homework assignment and measure the proportion in each class that complete the assignment
5. Compare batting averages of two baseball players
6. Time how long it will take kids to walk to the pool and back
7. Prices of items at clothing stores (found through browsing catalogs online)
8. Number of each type of animal cracker per box
9. How long it will take you to sort beans on to bulls-eyes with a dominant/non-dominant hand
10. Give the ol' Memory Experiment(groups rate sentence on how hard they are to pronounce/how easily they can form a vivid mental image) and compare number correct for each group
11. Count the number of each color of M&M you receive in a sample of M&M's
12. Change drop-height/rotor length of paper helicopters and record the time it takes to fall

After you spend about a week or so doing data collection, ask students to reflect on how data was collected. Notice also that some activities are done the same way (measuring proportions/means).  I'm fairly certain this has to be done to guide reflections, make kids confused, and ultimately learn something about making generalizations (mathematical modeling at its finest).

Ideas for Reflection:

1. What was measured in each data collection?  How does it compare with other types of data?
2. Which activities were useful for making comparisons?
3. If we're not making a comparison, what can we do with the data we collect?
4. Does it matter than some samples are smaller than others?  
5. Create a display for each activity with the raw data.  Which models tend to be the most appropriate?

I can see this being two weeks of AP Stat where kids think about collecting data and fitting similar models to similar methods of data collection.  Once they start fitting models to each situation for comparison, then you bring about some hypothesis testing procedures.

If you're a Stat teacher or not, provide your suggestions and ideas for data to collect.  It'd be great to get a new type of data to collect from somebody outside of the Stat realm.

AP Stat Lesson: Type I and Type II Errors

THE EXCEL SPREADSHEET
Type I and Type II Errors (housed on Box.net...is there a better way to do this?)
Directions for the activity contained in the spreadsheet.

SKILLS ADDRESSED
Statistical significance, Confidence Intervals related to hypothesis tests, Type I Error, Type II Error, Power, Alpha, Beta

THE CONTEXT
A factory is producing pharmaceutical grade glass vials.  Quality control engineers are employed to see if the factory is producing items at or below the industry standard of 5% defects.  They conduct a sample of size 100 (Mistake #1: I know this violates np>10, but it turns out that you wind up failing to reject a lot and it leads to a good understanding of Type II error) and determine the proportion of their sample that is defective. (Mistake #2: sampling 100 items and getting a proportion defective of 0.063 defective is impossible.  They will need to round to a whole number of successes when using the graphing calculator.)  Based on the results of this hypothesis test, they will decide if the factory must undergo a quality control review or continue with business as usual.


THE ACTIVITY
1ST PART - CONDUCT THE TEST, DECIDE WHETHER TO REJECT OR FAIL TO REJECT
It's dynamic.  Each kid will receive a randomly generated proportion.  They may do this up to 50 times.
First part of the activity: conduct the one proportion z-test using your graphing calculator.

2ND PART - DECIDE IF YOU MADE THE RIGHT DECISION
Unlock the spreadsheet (password: apstat5).  Have them change the fill color of the "True Proportion" column to reveal the true proportion of items that are actually defective.  They then evaluate their decision as to whether it was correct or incorrect.  Cue a whole class discussion on the 4 different scenarios of errors, then slap the AP Stat vocabulary on.

REFLECTION
Two huge mistakes that led to an amazing understanding of errors.  An overly planned lesson would have avoided these mistakes.  It also would not have generated a discussion on appropriate assumptions and conditions for inference.  An overly planned lesson would have also not brought up the question of "How come I'm failing to reject so much when it's false?"  An awesome comment: "I would not have learned this that well if I didn't have to think about those things."

This was 3 days worth of 46-minute classes.  Let's see how they do on the assessment of these skills.

THE SLIDESHOW

10-11 Errors

View more presentations from christjt.

Coming soon to this post...
The Google Form Assessment
A better version of the spreadsheet that allows any null hypothesis and any sample size.
100 comments on how to make this even better (hopefully)

AP Stat Lesson: Confidence Intervals (Graduation Party)

The Excel file: Graduation Party simulation.

What this Excel file does is simulates a student sending out 1500 invitations to a graduation party.  There is a true proportion of people that will attend, but it is unknown (see the "Population" tab of the Excel spreadsheet is completely blacked and password protected).  If you'd like the unlocked version, feel free to get in touch with me and I can send it along.  Students will conduct samples of 20, 50, and 100 to estimate the true proportion, and once they've generated a sufficient number of each sample size, they'll take a guess as to what the true proportion is.  Discussion follows as to which sample was most helpful to make the guess from.  Most guesses are that the true proportion is between 0.2 and 0.3.

They choose one of their sample proportions for sample size 100 and create a confidence interval for 4 different confidence levels: 68%, 90%, 95%, 99.7% (not randomly thought up by any means).  I chose these confidence levels because in the past I've seen students not associate confidence intervals with a middle percentage.

Collect students intervals using this form: One-Proportion Z-intervals Data Collection Form 
Display their responses here: One-Proportion Z-Intervals Raw Data (pay attention to both tabs, one has intervals and one has whether or not the interval captures the true proportion)

Once they've done some thinking, they will open this Excel file(One-Proportion Z-intervals Displays of Each Interval), providing a visual of each confidence interval.

We follow with having students lead their own discussion.  They'll begin by posting comments to a specific page of the class wiki, in order to get them to jot down an initial reaction to see if what they thought still holds up, or if their thinking needs revision.  A whole class discussion follows, and I challenge them to not allow me to speak for 10 minutes.  This can be difficult for me, but it is extremely difficult for them.

AP Stat Lesson: Unstructured Investigation

Give kids this: Hank Aaron - Home Runs by Pitcher

Let all hell break loose.

I've become quite a fan of "unstructured time" as of late, and I think this is perfect for an AP Statistics class.  I can see my baseball fans in class leaping at this opportunity to explore some baseball stats.  Whatever they wish to investigate, they are free to do so.  For the non-baseball fans, it may be just an opportunity to learn something about baseball.  I owe them some data on what they're interested in.  I look forward to hearing what a student that knows very little about baseball has to say.

Possible investigations:
1.  Comparison of Barry Bonds(or any other great home run hitter) to Hank Aaron. 
2.  Are pitchers today better (as a whole) than the ones Hank Aaron faced? (this comes from listening to Colin Cowherd say that Babe Ruth hit his home runs against guys who drove a milk truck in the off-season)
3.  Just how biased is this website?

Let them come up with how they're going to do any of the above. 

You Say It Best When You Say Nothing At All (about Hypothesis Testing)

I really like sharing things that work really well.  I don't know if it's a good idea on it's own, but this worked great considering we've done a lot of remediation (for students that needed it) and a lot of projects that delve deeper into statistics.  They are working with basics of statistics all the time, so tying it together into making statistical inferences is fairly easy when they have a good foundation.  I'd also like to think it has something to do with the way we've interacted with hypothesis tests in class.

Thumbtacks - Introduction
It begins with this form (Inference for Proportions) and handing out one thumbtack.  In their own brain, students decide what they think it is and what it would take to convince them it was wrong.  Then they toss the tack to be able to compare their observations to a model they've developed.  Sounds a lot like your entire hypothesis testing/inferential statistics unit.

The NCAA Basketball Tournament - A Basic Example
Kids then made predictions for the NCAA tournament and we tested just how good they were at doing so by comparing their proportion of correct first round picks to randomly guessing (p = 0.5).  A big question that came up was "Are we just doing this for the first round?" and in true teacher fashion I said, "Yes.  Now how come we're only doing it for the first round?"  Cue a killer discussion about large enough sample sizes and the Success/Failure condition.

Back to Thumbtacks - Put it into practice
Fire up the laptops and open up what the rest of your classmates thought (What They Thought).  Immediately they began to think "Why did this kid think they were incorrect when they got a lower proportion that what they thought they needed to be incorrect?"...a not so formalized way to think about a standard of proof and a low enough p-value to reject the null hypothesis.  This was one of those points in class where I said nothing and let their brains piece together what they were looking at.  I clarified what we were looking at, asked them to pick case that they thought was theirs and test the original hypothesis.

Conclusions
On the board, write your p-value and whether or not you rejected your original hypothesis.  As a class we'll have a look at everyone's p-values and decisions, then decide who has correctly rejected/not rejected.  They all argue about what p-value is considered "low enough" that you have to reject.  One of those moments where again, I say nothing and they develop an understanding of alpha-levels.  Not so formal...yet.

Projects/Practice

Pick another one of those contexts from the Inference for Proportions form and investigate it.  I think I'm going to add some more situations/contexts.  I'm also not sure that they ever need to fill out that form more than once...

What's Left to Do?
Sit back, relax, and let the 5's on the AP exam roll in.  Dress it up.  Put all the formal AP Exam terms/vocab/stuff to what they've already understood.  Then....
1.  So what really is the true proportion (Confidence Intervals)
2.  Is what we got really that different? (two proportions)
3.  Repeat procedure for sample means instead of proportions

Feel free to go to our class wiki for any supplemental exercises/materials.

Challenges of Project Based Learning (PBL) in AP Stat

Doing project based learning (PBL) in AP Stat this year has been a challenge. Ultimately, the best part about it is the learning experiences and opportunities it provides students. Every time a project is completed I think of 300 things that could be changed to make it, excuse me for using the phrase "100% better" (kind of an inside joke).  Below I've listed my major concerns about these projects, and the solutions I'm considering.  Your input on any of these is greatly appreciated.

Concerns and Solutions

1. The project was not rigorous enough. It covered too many skills too broadly, or too few skills in unnecessary depth.

     I want to make sure I create a sample project for each project to see just how in depth the projects go. I'm guilty of doing a bare-bones project example (okay, sometimes not even one at all).  There, I said it, I don't always do the project I assign.  The reason for this is to learn alongside of my students.

2. Some kids put a lot of work into a project that just doesn't really address much content, does so incorrectly, or doesn't really get into depth.

     Do it over. It's worth the learning experience of starting from scratch and completing the project again. 

3. What are they actually learning and can they replicate it

     Most of the time a project will involve them learning a new piece of technology as well as learning an AP Stat concept in greater detail.  I'm not sure these projects translate very well to getting an answer correct on the AP exam. Honestly, I want my projects to be far removed from getting right answers on an AP exam.

The Stat Project Process

1. Skills Organization - lay out the content related skills you will be addressing in your project

     Example: conditions for using the binomial/geometric probability distributions, calculating probability for each distribution, determining expected value and standard deviation for a probability distribution

2. Place context on each skill - group brainstorming to see what context fits each skill the best

     Example: highlight the difference between the two probability distributions by filming students walking downthehallway until we observe one of them wearing earbuds (geometric). Compare with a binomial distribution, showing 10 kids walking down the hall, 5 of which are wearing earbuds. 

 

3. Storyboard/Product: what multimedia can we put together, how does it flow, how does everything fit together?  

     Here's where students choose a tool that meets their project's needs.  

4. Edits - does anything need to be rethought or redone as something better?  

     High school students seem to miss this step in almost everything they do, once the "be done" mentality takes over. Sometimes the "do it over" option is the best learning experience.  I've found I've spent more time suggesting they edit and critique their own work and each others' work, and it's made a world of difference in overall quality of product and understanding of statistics.  

Since I don't believe in giving deadlines for learning, when a student asks when their projects are due, I tell them that they may turn them in whenever this process is completed.  With most projects I honestly don't think this process is ever completed.

No Decorations in my Classroom

I don't decorate my classroom. I've referred to it as "hospital" sterile when asked what my room looks like.  The only decorations I'd like to have in my room are signs that say: "LEARN FROM THE PERSON NEXT TO YOU".  My philosophy on this is that it shouldn't matter what's on the walls, let's start caring about what's happening inside the walls.  If it's really cool, then kids will start hanging stuff on the walls and decorating the room the way they want to.

A  few years back, I had a student that would draw pictures to hang on the wall, half of them were about AP Stat. All of them were entertaining. The ones that were about stat were amazingly good depictions of AP Stat topics.  Stay tuned for me to scan these images in and post the best of them.

I think we're in trouble if we concern ourselves too much with what the content looks like, rather imthan what the content actually is. Make that double if we use technology to change only what the content looks like.  When I choose a technology tool, I want tools that make students think deeper first, and ooh and ahh later.  This is probably why I choose Wikispaces, Google Docs, then Microsoft Excel every single time.

I recently responded to a tweet from @nwhyluckysgirl regarding using emoticons when commenting on student work electronically.  

@nwhyluckysgirl: "when commenting on student work electronically, do you use emoticons?" 

@jasonchri: "the occasional emoticon, not too often.  The comment usually is seen only for the emoticon"

My fellow tech integrator and I often debate look and feel, mostly on the look and feel of our district's technology wiki, NP Tech Tools. I keep my class wiki as the default background and format, and I honestly don't care to spend time choosing the right template/background/picture. The content of my class wiki should be the focus, and for that matter I would hope that's what's interesting about it. If you're reading this blog,  you'll see that I take a similar approach to blog layout (and have not yet switched to word press).  How are  you going to see the content if there's a thousand other things to look at on the page? 

I was inspired to write this after reading a brilliant post(Coloring Books or Canvasses? from Spencer's Scratch Pad about technology that makes students think deeply about a subject. Use tech to make students think more, not think about something else, not comment on how weird or cool something looks.  

Making the choice of what tech tool you want to use needs to be content driven.  I wind up picking one of the same three tools (Wikis, Google Docs, Microsoft Excel), since experience has shown these tools can stimulate conversation and let students think the way that they want to.

Some of my tricks...

1.  An Excel spreadsheet that is completely protected, so that they can only manipulate and change certain values to notice some patterns.  They'll need to think their way through certain processes too, not simply plug-in numbers and tell Excel to perform a calculation. 

2.  A massively shared Google document to write about the difference between two(or more) topics.  I'm trying this to get an entire class to discuss the difference between binomial and geometric distributions. 

3.  Class wiki- set of skills completely blank, so determine just how to organize lessons and what we've thought about

I'm branching out...

Forever I've wanted to use more and more multimedia ideas in my class.  Not just make a music video (a lot of times kids spend a ton of time on creating a video, and frequently miss the boat on content).  I want students to show me everything they know about probability, but do so in a very short video (30 sec - 1 min).

I'm going to suggest Animoto, but I really want to allow them to pick any tool that they should find, as long as it communicates everything they know about probability.  I also want to have them use pictures that they've taken, just to get them thinking a little bit more.  

I want to come up with the best web tools/tech tools for education, and I think this is how I want to start. Which tools make students think more, and think deeper? Which ones accomplish the same thing as a "solve for x" worksheet?  Do certain tools get misused?  Are there some tools that are all bark and no bite?

Today's AP Stat Lesson: EXCEL HEAVY - VLOOKUP(RANDBETWEEN(NERD, GEEK), STATGEEKS,2)

Today's(tomorrow's) plan for AP Statistics is a little Excel heavy,  something that I hope carries over for my students into college and beyond. Is there a standardized test that measures a student's increased proficiency at Microsoft Excel, or other computer apps for that matter?  Most commands involve looking up a value at random between zero and one hundred.

Each student has been keeping track of the number of sheets of paper received in each class, each day, over the span of about 2 months. The focus is on teacher created paper, so if a student uses a piece of their own notebook paper it doesn't count.  Incidentally, om pretty sure that AP Stat is dead last for every one of my students major subjects (AP Stat instructor pats himself on back).

Using this info, they are going to create a probability model for the number of sheets of paper received for a single class.

For AP Stat...

SHEETS OF PAPER    0     1      2 

PROBABILITY         0.90 0.05 0.05  

Now that the probability model is created the Excel fun can begin.  Number all cells in one column from 1-100 to represent a possible outcome. Place each possible outcome in the second column according to it's the probability you observed. Example: in the chart above, the probability of receiving 0 sheets of paper was 0.90, so spaces 1-90 would be 0. The probability of receiving 1 was 0.05, so 91-95 would be 1, and 96-100 would be 2.  Repeat for all other possible outcomes. Suggest to students that they choose a class that is at least manageable as far as different numbers of sheets of paper.  Yes, there is a way to make Excel do this, but that is a little too awesome for an AP Stat class.  

Create a new sheet for simulating new days of each class. For the first day, we are going to "lookup" random values from the previous sheet to see how many sheets of paper we will receive. The command for doing this... VLOOKUP(RANDINT(1,100),in the previous sheet, give the value in the second column in the row that the random number is in). 

Example:  =VLOOKUP(RANDBETWEEN(1,100),Sheet2!A$1:B$100,2)

Keep the dollar signs so that when you drag to autofill the formula they continue to look within the same array of cells. Autofill about 200 or 300 of these cells...or 500 :)

Next we're going to calculate the average number of sheets of paper we've received each day. AVERAGE(cell to the left and all cells above). 

Example: =AVERAGE(B2:B6)

Now we can look at the average over the long run (1000 days, or even more) and begin to build our definition of Expected Value.  Then, later, we'll do expected value the easy way in Microsoft Excel using the formula.  I wanted them to wrap their brains around the definition of Expected Value before they began using the formula: E(X) = SUM[X*p(X)].  It's pretty cool to see just how long of a run you need to make the simulation average approach the expected value.

The lesson is a bit like a cooking show, but it's the first time we are in Excel. The kids use their own data, so that's enjoyable/unique for most of them. The bigger idea of simulating outcomes is very powerful in learning statistics. I love nothing more than a student centered approach, but I would hate to say "discover how to use vlookup and randint functions in Excel. If anyone has a way to take a constructivist approach to learning Microsoft Excel, I'd love to hear it.

The Excel spreadsheet that students create

My Test with No Right Answers

At the slightly more than halfway point in the year, I decided to give my students an assessment on skills we would have learned previously this year.  In an AP Stat class, this type of exercise is meant to take the place of the 2 weeks of "review" that most educators wind up with at the end of the year before the AP Exam.

Here's the test: AP Statistics Mid-Year Assessment .  Using this link (and excusing the poor formatting that comes with inserting images into Google docs) they are to create a Google Doc and share it with me that is essentially their stream of consciousness  statistical reasoning.  They were permitted to use the class wiki, their Stat textbook (BVD - Stats: Modeling the World), and any other online resources available to them.  Big thanks to David Wees (@davidwees) for the data, graph, and the article!

They were not permitted to use each other as a resource, as this was an assessment to see what they know as individuals.  This makes me uncomfortable, since it doesn't necessary follow the cooperative model I've we've built the classroom on.  Next time I give an assessment, I'll allow them to use each other as a resource as well, but the task needs to be uber-authentic.  Suggestions?
I'll share a conversation I had with a student about this, since it made my day.

"Mr. C, can we use each other as a resource?" - Student
"I'd prefer not, since I want to see what you know." - Me
"But in 'real life' we'd be allowed to use each other." - Student
"Arrggghhh, why must you make that argument?" - Me
"Because you taught me to." - Student

First thing a Stat teacher, or anyone familiar with Statistics will notice is that for most of the questions there's not really one "right" answer.  The purpose behind this is to allow kids to think and write what they know, in regard to the skills being assessed.  I'm loving the thought that has gone into each response.  It feels like I've really touched on something here, something that does a little bit better than the strategy of "write everything you know about the topic" for the poor test taker/assessment do-er.

So what resource did kids use the most?  At quick glance, my class wiki comes in first, with the Stat textbook coming in second.  I'm hoping this spurs more content creation on the class wiki, so that it can develop into the ultimate online stat textbook.  Yes, I am still living that dream.

"AP Kids" are not the only ones who need quality learning experiences

After hitting the Google Reader hard while at Subway the other day (probably should've been eating lunch and relaxing instead of working) I was inspired by @InnovativeEdu's post on asking kids to design their own learning. Having just switched to the project-based learning format for my classroom, I love to share what my students are doing at these professional development sessions we conduct.

The question that always comes up is "Yeah, but what level do you teach?"  When my response is AP Statistics, it's immediately dismissed since "they are AP kids."  So what if I said, "I had this great lesson where I stood and lectured for 46 minutes with zero audience participation!"  I can almost guarantee to have the same response, "Well, your lecture worked so well because they're AP kids, no way that would work with my 4.0's!"

As an educator in a professional development workshop, why not spend that time to think of ways to reach the kids that are not "AP kids".  It seems like that would be a better use of time than to confirm your suspicions that there just isn't anything that works to educate those that are not taking Advanced Placement courses.

The students in 4.0 classes are the ones that have been most vocal about being not interested in what you have to say.  They are students that are completely unwilling/unmotivated to work unless it interests them.  Know what is especially uninteresting...x's, y's, and slopes of lines.  But these lower level courses cover basic equation solving and "find the slope" the exact same way, over and over again from the time the student is in 9th grade until 12th grade.

Great lessons, quality education, and interesting projects shouldn't be reserved for the best and brightest students.  The 4.0 students don't need more lectures and more basic junk that they don't care about.  They need to be interested, first and foremost.  They don't need more discipline or a rigid classroom structure.  They've told you 100 times that they hate that environment, so stop imposing it on them.

When I see my "AP kids" work on a project that they're excited about (sampling teachers in the school to see if they have tattoos, experiment on whether or not people can walk and text, see how often radio stations repeat certain songs) they aren't excited about it because they're "AP kids".  They aren't excited about it because I threatened them with detention if they showed a lack of enthusiasm.  They're excited about it because they had the choice in what they wanted to do.  They're students, there is no way they are so drastically different than their peers that just so happened to not do well in one math class so they were forced to slide down the ladder and be stuck in "4.0 world".

Oh, and they learn way more from me doing their own projects than they ever could from answering some multiple choice and some free response questions for me.

Reassessment Fridays (SBG): A Love Story

“Every student did their own thing in class today.”
How often is that the summary of a mathematics class?  How about an art class? 


Today was the standard reassessment day for my AP Stat classes.  I wasn’t sure how I was going to let students reassess when I started Standards Based Grading.  I’ve come up with using every Friday as a reassessment day.



I let students pick 2 skills to reassess on.  They pick them Wednesday, I create reassessments Thursday, they take them on Friday.  The reassessors are given a mail merged document that is their assignment for that day’s reassessment.  Should they choose not to formally reassess in class, they always have the option to do a project on their own to show their mastery of any of the skills they have learned.  This has been a system that works for the students that want to reassess, but it works even better for those not reassessing.


Today about a third of each class was reassessing.  So what do the other students in class do?  They play.  They learn.  They collaborate:

1. One student began conducting simulations to simulate random clicks in Minesweeper.  Two others quickly became interested and a Minesweeper collaborative was born.
2. About 10 different students were editing 10 different pages of the class wiki to make it an online textbook.  
3. They were gathering data for different projects they hope to complete later in the year
1. a project where they wish to determine the proportion of teachers at school that have tattoos
2. simulating hands for various different card games
3. the true proportion of dives by a diver that are “ripped”

I look forward to my “Reassessment Fridays” because of the classroom vibe.  I’ll provide a few ideas for what can be worked on, then they get started doing things that they want to do.  Today’s ideas: Conduct a simulation, finish an old project, start a new project, edit the class wiki, create models of data collected this week.  I’m immediately working on making this the classroom activity for every day, not just Friday.  


My favorite part about it is that I am providing them time to be as smart as they want to be in class.  I’m not tricking them into learning with some gimmick.  I’m not having them finish a worksheet for points.  I’m not asking 26 of them to answer the same question.

First Day of School Lesson Plan

So here's my contribution to the slew of first day of school posts in the edu-blogging world.

I want to start my year by creating a climate of collaboration, friendliness, INFORMALITY(in school? you're crazy!).  From day one, I want my students to begin to take ownership of the class.  There is more than one person to learn from in the room, in fact, there's 30...and millions of others easily reached online, but that's for another day.

Something I will definitely do differently this year is not go over the grading policy immediately.  My main reason for this is that I want to set a tone of a collaborative environment, not that of a teacher saying, "This is the way it's going to be, there's the door if you don't like it."  Why would we want to start a year believing a class is difficult, instead of developing that conclusion on our own?

So, yes, you will have homework an assignment given the first day of class.  It's not going to be Read pgs 1-100 and do ALL odd exercises once you've completed your outline.  Your homework assignment will be to read my grading policy (Standards-Based all the way!) and be prepared to discuss it with your group members and with me.  If you're not going to read it or formulate ideas, how (more importantly, why) should we allow you to contribute to the class discussion?

So, what will we do the first day?  Probably get to know each other.  Once we're all comfortable with a learning community instead of a classroom, then we'll start with the content.  AP exam in May you say?  If you're not worried than I'm not.

Anatomy of a Makeup Test & Stimulus Package

So you were absent on test day...cue dramatic trombone (you know, wah wah)...for whatever reason: Sickness, family, local sports team championship parade, whatever. So what happens now? Do you get a grand reprieve of having to take the test later than everyone else?!?!?! Let's explore what happens when you are absent on test day (let's say test day was a Monday).

1. You come into school next day (Tuesday) and say "Hey Mr. C, when can I make up that test?"
2. Mr. C, automatically knowing your schedule from memory (like he does for all 112 of his students) says "How about during lunch?"
3. Your response, "Well, I am making up a Psych quiz then, and I have a chem lab to makeup during study hall, and it's a full moon, and I have band practice, then I work, then I have basketball, then I have fun time, so how about Friday?
4. After much debate and discussion of schedules, you get the great idea to make it up after school. Now the after school makeup is tricky.

• Mr. C needs to bring YOUR test to the math planning center
• He must also remember to bring your formula sheet
• He must inform his colleagues that there is a test in his mailbox for this one exceptional student
• Student takes test in a hallway - great testing environment
• Student could conceivably take 85 minutes to take test
• Mr. C checks his mailbox the next day, and puts your test into his makeups to grade

Now multiply this process by 10 students (that is how many missed last week's test). Is this not insanity? From a management standpoint, I got kids coming left and right to make up tests. Can we make everyone's life easier and just not be absent on test day?

Onto the stimulus package. Our current US president is now traveling the country to "sell" the stimulus package to different communities. Most view this as, "Hey, what a cool guy! He is so relatable. He's going to come around and tell us exactly what is in it, and how it's good for us." Didn't we elect this guy to act on our behalf? That is to say, does he NEED to sell it to us? He is our president, we have put our faith in him to act in the best interest of the country, why must he travel the nation to sell this to us? The fact that there is a feeling that it needs to be sold should raise some eyebrows from all citizens, not just the hardcore conservatives.

If anyone has an itemization of what is in this stimulus package, can you e-mail me where it can be found, or post it as a comment here? I have a cool activity we can do with it as a class. I'd like to break this thing down.

-Mr. C

When the kid doesn't pass...make passing easier?

STOP!!!!! Read this article before continuing

So your student got a B+ in a rigorous, difficult, challenging environment. This is unacceptable because it is not an A?!?!?! So what's the solution... Fight fight fight and make it easier to get an A. I hope I am not the only one that sees something terribly wrong with this. Please consider the following situations as they relate to this article...

So apparently I have heard that there are too many people failing the PA Driver's License Exam. The solution is that those failing the test got together and fought PennDOT, successfully changing the driver's test requirements to: drive forward 100 ft, put the car in reverse, turn on the windshield wipers, successfully make a right-hand turn. Immediate ramifications are not known.

SAT's have come under fire because so many students are not meeting their college's SAT requirements. Let's get together and make the SAT an easier test. That way, more kids will get higher scores and be qualified to get into the colleges that they want.

The end result from both situations is an "inignoranted"(totally made that word up) population. Okay, so the driver's license one is a little far-fetched, but I'm not sure the SAT example is totally out of line here.

Rigor is what makes the best the best, the not-so best the not-so best, the average the average, and so on....Without rigor we have no means of determining who the best is, we just are certain that everybody can achieve the standard, and nobody has demonstrated greatness. These parents have defined "fairness" as "everyone gets a trophy/everyone gets an A". An A is exactly that, achieved by the best and brightest, some work really hard to arrive there, some do not need to. Not once in this article was it mentioned that parents encouraged their kids to get better...do a little bit more to get that extra 2 percentage points to EARN the A.

It is often confusing about "Who deserves an A", and I think that definition is different between parent, teacher, and student. Parent and student share a similar definition...my kid works really hard so they deserve an A. In an odd counterexample, what if they work really hard and are learning the concept(s) the wrong way? Should these hard workers not be accountable for content knowledge? Teacher definition of an A is essentially the students that show high-level mastery of content. If that is debatable (that 89%), work-ethic is examined...the rationale of which is that if the student is a hard worker, they will eventually achieve high-level mastery.

In conclusion, I feel the need to address my grading practice. In my gradebook, pre-homework/project grade, there were about 10 kids that had an A average. This pre-homework/project grade is fairly indicative of your master of content. In terms of the AP Exam an A pre-HW would indicate a 5, B a 4, C a 3, D a 2, and F a 1. This is something not set in stone however, and with some preparation for the AP Exam through use of a review book(Barron's) can increase your exam score by 1 to 2. After homework and project, your grade reflects the amount of work that you have done, and the quality of product you have produced. This is minimally relevant to taking the AP test, but very necessary for your future development (college/career).

My job as an educator is not to give you an A, it is to prepare you for college. You need to be put through a high level of rigor so that when you get to college, you have been exposed to a rigorous courseload. If we are not rigorous in our teaching practice, we are not preparing you for college. Relaxing our standards would indicate that we are sending you to college less prepared.

Happy Snow Day,
Mr. C